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That's only true if the fractions are "proper" fractions ... with numerator smaller than denominator. The reason is: If you take (a piece less than the whole thing) out of (a piece less than the whole thing), you wind up with a piece smaller than either of the original pieces.
A fraction is smaller than one if the number on the top is less than the number on the bottom.
Fractions smaller than 1/8: 1/9 1/10 1/11 1/12 1/13 1/14 1/15 1/16... You get the idea. Just keep increasing the denominator, because any fraction with a numerator of one but denominator that is greater than the fraction you're comparing it to will be smaller in value than that fraction.
if 1/2 x 1/3 then times it and get 1/6